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About
President
Governance
Partner Institutions
Visit
People
Management
Faculty
Postdocs
Visiting Scholars
Staff
Research
Research Groups
Courses
Seminars
Join Us
Faculty
Postdocs
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Events
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Forum
Life @ BIMSA
Accommodation
Transportation
Facilities
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News
News
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Qiuzhen College, Tsinghua University
Yau Mathematical Sciences Center, Tsinghua University (YMSC)
Tsinghua Sanya International  Mathematics Forum (TSIMF)
Shanghai Institute for Mathematics and  Interdisciplinary Sciences (SIMIS)
BIMSA > Topics in Representation Theory Fluctuations of Young diagrams for symplectic groups
Fluctuations of Young diagrams for symplectic groups
Organizers
Semen Artamonov , Pavel Nikitin , Shamil Shakirov
Speaker
Anton Selemenchuk
Time
Friday, January 24, 2025 1:00 PM - 2:30 PM
Venue
A14-201
Online
Zoom 242 742 6089 (BIMSA)
Abstract
Consider an n×k matrix of i.i.d. Bernoulli random numbers with some value of p. Dual RSK algorithm gives a bijection of this matrix to a pair of Young tableaux of conjugate shape, which is manifestation of skew Howe GLn×GLk-duality. Thus the probability measure on zero-ones matrix leads to the probability measure on Young diagrams proportional to the ratio of the dimension of GLn×GLk-representation and the dimension of the exterior algebra ⋀(Cn⊗Ck). Similarly, by applying Proctor's algorithm based on Berele's modification of the Schensted insertion, we get skew Howe duality for the pairs of groups Sp2n×Sp2k. In the limit when n,k→∞, GL-case is relatively easily studied by use of free-fermionic representation for the correlation kernel. But for the symplectic groups there is no convenient free-fermionic representation. We use Christoffel transformation to obtain the semiclassical orthogonal polynomials for Sp2n×Sp2k.
Beijing Institute of Mathematical Sciences and Applications
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